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Description: Compositional hierarchical structure is a prerequisite for productive languages; it allows language learners to express and understand an infinity of meanings from finite sources (i.e., a lexicon and a grammar). Understanding how such structure evolved is central to evolutionary linguistics. Previous work combining artificial language learning and iterated learning techniques has shown how basic compositional structure can evolve from the trade-off between learnability and expressivity pressures at play in language transmission. In the present study we show, across two experiments, how the same mechanisms involved in the evolution of basic compositionality can also lead to the evolution of compositional hierarchical structure. We thus provide experimental evidence showing that cultural transmission allows advantages of compositional hierarchical structure in language learning and use to permeate language as a system of behaviour.